208 DETERMINATION OF AN OHBIT FROM [BOOK II. 



Hence 



log (tan cos (a&quot; / ) tan /?&quot; cos (a I }) = log Tsm t 8.5786513 



logsin(&quot; a)=lo g rcosi! .......... 8.7423191 



Hence t 145 32 57&quot;.78 log T ....... 8.8260683 



= 337 30 58.11 log sin (* + /) .... 9.5825441 n 



Lastly 



log (tan sin (a&quot; f ) tan (3&quot; sin (a f)) = log . . 8.2033319 n 

 log T sin (* + /) .............. 8.4086124 n 



whence log tan (d r a) ............ 9.7947195 



&amp;lt;T _ a = 31 56 11&quot;.81, and therefore a = 23 13&quot;.12. 

 According to article 140 we have 



y d&quot; = 191 15 18&quot;.85 log sin 9.2904352 n log cos 9.9915661 

 ^ &amp;lt;? =1944830.62 &quot; 9.4075427 n 9.9853301 



&amp;gt;_^&quot; =1983933.17 &quot; &quot; 9.5050667 n 

 &amp;gt; tf -f a = 200 10 14 .63 9.5375909 

 &amp;gt;&quot; d =191 19 8.27 &quot; 9.2928554 w 

 A D&quot;d + a = lW 17 46 .06 9.2082723 n 



Hence follow, 



log a . . . 9.5494437, a =+0.3543592 

 log* . . . 9.8613533. 



Formula 13 would give log b = 9.8613531, but we have preferred the former 

 value, because sin (A D d -\-o) is greater than sin (AD&quot; - 8 -\-a). 

 Again, by article 141 we have, 



3 log # sin d . . . 9.1786252 

 log 2 ...... 0.3010300 



log sin a ..... 7.8295601 



7.3092153 and therefore log c = 2.6907847 



log* 9.8613533 



log cos a 9.9999901 



9.8613632 



